## When Do The Quadratic Polynomials px^2+qy+r and 2px^2+qy+r Both Factor?

### Item

#### Title

When Do The Quadratic Polynomials px^2+qy+r and 2px^2+qy+r Both Factor?

#### Description

One mathematical skill developed in a high school algebra class involves factoring a quadratic polynomial into a product of two binomials. For example, x^2+17x+30=(x+2)(x+15). If a 2 is placed in front of the x^2, the polynomial 2x^2+17x+30 factors as(2x+5)(x+6). A good exercise for students is to find other quadratic polynomials px^2+qy+r and 2px^2+qy+r that both factor. A pair of quadratic polynomials with this property is called a quadratic doublet. The first part of this talk will characterize values for p, q, and r that yield quadratic doublets. A Pythagorean Triple is three whole numbers a, b, c with the property that a^2+b^2=c^2 . The second part of the talk will show a connection between the quadratic doublets and Pythagorean Triples.
Vincent Ferlini

#### Contributor

Keene State College

Brooke Hatanaka

2015-04-11

#### Identifier

http://hdl.handle.net/20.500.12088/7602

en_US

Mathematics

Presentation

#### Rights

http://rightsstatements.org/vocab/InC/1.0/